Geodesic
Normal solvability of a class of differential equations of infinite order
Sbornik. Mathematics, Tome 13 (1971) no. 3, pp. 371-399 Cet article a éte moissonné depuis la source Math-Net.Ru

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In this article we study a differential equation of infinite order with polynomial coefficients \begin{equation} Ly\equiv\sum^\infty_{k=1}P_k(x)y^k(x)=f(x),\qquad P_k(x)=\sum^{n_k}_{s= 0}a_s^k x^s, \end{equation} where $\varlimsup_{k\to\infty}\frac{n_k}k=\alpha<1$. Under given conditions on the coefficients $a_s^k$, normal solvability of equation $(1)$ is established in the class of entire functions $[1-\alpha,Q]$, where $0 and $Q$ is determined by the coefficients $a_s^k$. Bibliography: 10 titles. 
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Yu. F. Korobeinik; O. V. Epifanov. Normal solvability of a class of differential equations of infinite order. Sbornik. Mathematics, Tome 13 (1971) no. 3, pp. 371-399. http://geodesic.mathdoc.fr/item/SM_1971_13_3_a3/

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[9] Yu. F. Korobeinik, “O preobrazovaniyakh analiticheskikh prostranstv s pomoschyu differentsialnykh operatorov beskonechnogo poryadka”, Uspekhi matem. nauk, XX:5(125) (1965), 208–213 | MR

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